MARC Record from marc_columbia

LEADER: 04754cam a2200457 i 4500
001 10249636
005 20131118210830.0
008 130225s2013 riu b 000 0 eng
010 $a 2012045837
020 $a9780821891520 (alk. paper)
020 $a0821891529 (alk. paper)
035 $a(OCoLC)ocn823209440
035 $a(OCoLC)823209440
035 $a(NNC)10249636
040 $aDLC$beng$erda$cDLC$dYDXCP$dOCLCO$dDAY$dBWX$dTXA$dORZ$dMUU
042 $apcc
050 00 $aQA295$b.G485 2013
082 00 $a515/.353$223
084 $a42B25$a35A23$a26D10$a35A15$a46E35$2msc
100 1 $aGhoussoub, N.$q(Nassif),$d1953-
245 10 $aFunctional inequalities :$bnew perspectives and new applications /$cNassif Ghoussoub, Amir Moradifam.
264 1 $aProvidence, Rhode Island :$bAmerican Mathematical Society,$c[2013]
264 4 $c©2013
300 $axxiv, 299 pages ;$c26 cm.
336 $atext$2rdacontent
337 $aunmediated$2rdamedia
338 $avolume$2rdacarrier
490 1 $aMathematical surveys and monographs ;$vv. 187
504 $aIncludes bibliographical references.
520 $a"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.
650 0 $aInequalities (Mathematics)
650 0 $aHarmonic analysis.
650 7 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory.$2msc
650 7 $aPartial differential equations -- General topics -- Inequalities involving derivatives and differential and integral operators, inequalities for integrals.$2msc
650 7 $aReal functions -- Inequalities -- Inequalities involving derivatives and differential and integral operators.$2msc
650 7 $aPartial differential equations -- General topics -- Variational methods.$2msc
650 7 $aFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems.$2msc
700 1 $aMoradifam, Amir,$d1980-
830 0 $aMathematical surveys and monographs ;$vno. 187.
880 0 $6505-00$aPart 1. Hardy Type Inequalities. Bessel Pairs and Sturm's Oscillation Theory ; The Classical Hardy Inequality and Its Improvements ; Improved Hardy Inequality with Boundary Singularity ; Weighted Hardy Inequalities ; The Hardy Inequality and Second Order Nonlinear Eigenvalue Problems. -- Part 2. Hardy-Rellich Type Inequalities. Improved Hardy-Rellich Inequalities on H2 0 (Ω) ; Weighted Hardy-Rellich Inequalities on H2(Ω) H1 0 (Ω) ; Critical Dimensions for 4th Order Nonlinear Eigenvalue Problems. -- Part 3. Hardy Inequalities for General Elliptic Operators. General Hardy Inequalities ; Improved Hardy Inequalities For General Elliptic Operators ; Regularity and Stability of Solutions in Non-Self-Adjoint Problems. -- Part 4. Mass Transport and Optimal Geometric Inequalities. A General Comparison Principle for Interacting Gases ; Optimal Euclidean Sobolev Inequalities ; Geometric Inequalities. -- Part 5. Hardy-Rellich-Sobolev Inequalities. The Hardy-Sobolev Inequalities ; Domain Curvature and Best Constants in the Hardy-Sobolev Inequalities. -- Part 6. Aubin-Moser-Onofri Inequalities. Log-Sobolev Inequalities on the Real Line ; Trudinger-Moser-Onofri Inequality on S² ; Optimal Aubin-Moser-Onofri Inequality on S².
852 00 $bmat$hQA295$i.G485 2013